Virtual Black Holes

One would expect spacetime to have a foam-like structure on the Planck scale with a very high topology. If spacetime is simply connected (which is assumed in this paper), the non-trivial homology occurs in dimension two, and spacetime can be regarded as being essentially the topological sum of $S^2\times S^2$ and $K3$ bubbles. Comparison with the instantons for pair creation of black holes shows that the $S^2\times S^2$ bubbles can be interpreted as closed loops of virtual black holes. It is shown that scattering in such topological fluctuations leads to loss of quantum coherence, or in other words, to a superscattering matrix $\$$ that does not factorise into an $S$ matrix and its adjoint. This loss of quantum coherence is very small at low energies for everything except scalar fields, leading to the prediction that we may never observe the Higgs particle. Another possible observational consequence may be that the $\theta$ angle of QCD is zero without having to invoke the problematical existence of a light axion. The picture of virtual black holes given here also suggests that macroscopic black holes will evaporate down to the Planck size and then disappear in the sea of virtual black holes.Comment: 24p, LaTeX, 3 postscript figures included with epsf sent in a seperate uuencoded fil

Open Inflation, the Four Form and the Cosmological Constant

Fundamental theories of quantum gravity such as supergravity include a four form field strength which contributes to the cosmological constant. The inclusion of such a field into our theory of open inflation (hep-th/9802030) allows an anthropic solution to the cosmological constant problem in which the cosmological constant gives a small but non-negligible contribution to the density of today's universe. We include a discussion of the role of the singularity in our solution and a reply to Vilenkin's recent criticism (hep-th/9803084).Comment: 11 pages, RevTex file. Replaced version contains major corrections, including a crucial new surface term, and important additions. A connection to eleven dimensional supergravity is made. The anthropic solution of the cosmological constant problem now holds with a real four form in the Lorentzian region. The previously claimed solution to the empty universe problem is shown to be incorrect, but a new solution is suggeste

Homogeneous Modes of Cosmological Instantons

We discuss the O(4) invariant perturbation modes of cosmological instantons. These modes are spatially homogeneous in Lorentzian spacetime and thus not relevant to density perturbations. But their properties are important in establishing the meaning of the Euclidean path integral. If negative modes are present, the Euclidean path integral is not well defined, but may nevertheless be useful in an approximate description of the decay of an unstable state. When gravitational dynamics is included, counting negative modes requires a careful treatment of the conformal factor problem. We demonstrate that for an appropriate choice of coordinate on phase space, the second order Euclidean action is bounded below for normalized perturbations and has a finite number of negative modes. We prove that there is a negative mode for many gravitational instantons of the Hawking-Moss or Coleman-De Luccia type, and discuss the associated spectral flow. We also investigate Hawking-Turok constrained instantons, which occur in a generic inflationary model. Implementing the regularization and constraint proposed by Kirklin, Turok and Wiseman, we find that those instantons leading to substantial inflation do not possess negative modes. Using an alternate regularization and constraint motivated by reduction from five dimensions, we find a negative mode is present. These investigations shed new light on the suitability of Euclidean quantum gravity as a potential description of our universe.Comment: 16 pages, compressed and RevTex file, including one postscript figure fil

Nonsingular instantons for the creation of open universes

We show that the instability of the singular Vilenkin instanton describing the creation of an open universe can be avoided using, instead of a minimally coupled scalar field, an axionic massless scalar field which gives rise to the Giddings-Strominger instanton. However, if we replace the singularity of the Hawking Turok instanton for an axionic wormhole some interpretational and technical difficulties would appear which can be overcome by introducing a positive cosmological constant in the action. This would make the instanton finite and free constant in the action. This would make the instanton finite and free from any instabilities.Comment: 8 pages, RevTex. A new section on the instantonic global structure and a figure have been added. To appear in Phys. Rev.

TASI Lectures on the Cosmological Constant

The energy density of the vacuum, Lambda, is at least 60 orders of magnitude smaller than several known contributions to it. Approaches to this problem are tightly constrained by data ranging from elementary observations to precision experiments. Absent overwhelming evidence to the contrary, dark energy can only be interpreted as vacuum energy, so the venerable assumption that Lambda=0 conflicts with observation. The possibility remains that Lambda is fundamentally variable, though constant over large spacetime regions. This can explain the observed value, but only in a theory satisfying a number of restrictive kinematic and dynamical conditions. String theory offers a concrete realization through its landscape of metastable vacua.Comment: 39 pages, 3 figure

On the Initial Singularity Problem in Two Dimensional Quantum Cosmology

The problem of how to put interactions in two-dimensional quantum gravity in the strong coupling regime is studied. It shows that the most general interaction consistent with this symmetry is a Liouville term that contain two parameters $(\alpha, \beta)$ satisfying the algebraic relation $2\beta - \alpha =2$ in order to assure the closure of the diffeomorphism algebra. The model is classically soluble and it contains as general solution the temporal singularity. The theory is quantized and we show that the propagation amplitude fall tozero in $\tau =0$. This result shows that the classical singularities are smoothed by quantum effects and the bing-bang concept could be considered as a classical extrapolation instead of a physical concept.Comment: 9pp, Revtex 3.0. New references added. To appear in Phys. Rev.

Why Does Inflation Start at the Top of the Hill?

We show why the universe started in an unstable de Sitter state. The quantum origin of our universe implies one must take a `top down' approach to the problem of initial conditions in cosmology, in which the histories that contribute to the path integral, depend on the observable being measured. Using the no boundary proposal to specify the class of histories, we study the quantum cosmological origin of an inflationary universe in theories like trace anomaly driven inflation in which the effective potential has a local maximum. We find that an expanding universe is most likely to emerge in an unstable de Sitter state, by semiclassical tunneling via a Hawking-Moss instanton. Since the top down view is forced upon us by the quantum nature of the universe, we argue that the approach developed here should still apply when the framework of quantum cosmology will be based on M-Theory.Comment: 21 pages, 1 figur

Dynamical conformal transformation and classical Euclidean wormholes

We investigate the necessary condition for the existence of classical Euclidean wormholes in a conformally non-invariant gravitational model minimally coupled to an scalar field. It is shown that while the original Ricci tensor with positive eigenvalues does not allow the Euclidean wormholes to occur, under dynamical conformal transformations the Ricci tensor, with respect to the original metric, is dynamically coupled with the conformal field and its eigenvalues may become negative allowing the Euclidean wormholes to occur. Therefore, it is conjectured that dynamical conformal transformations may provide us with {\it effective} forms of matter sources leading to Euclidean wormholes in conformally non-invariant systems.Comment: 6 pages, minor revisio

Classical and quantum wormholes in a flat Λ\Lambda-decaying cosmology

We study the classical and quantum wormholes for a flat {\it Euclidean} Friedmann-Robertson-Walker metric with a perfect fluid including an ordinary matter source plus a source playing the role of dark energy (decaying cosmological term). It is shown that classical wormholes exist for this model and the quantum version of such wormholes are consistent with the Hawking-Page conjecture for quantum wormholes as solutions of the Wheeler-DeWitt equation.Comment: 8 pages, 4 figures, accepted for publication in IJT

Ultra-fast image converter streak cameras for laser fusion diagnostics

The design and operation of a 10-ps resolution optical streak camera used to characterize laser pulses and other transient optical signals in fusion research is discussed. Performance characteristics are presented. The design, operation, and application of an x-ray streak camera used to study laser-produced plasmas in the x-ray spectral region of 1 to 10 keV with temporal and spatial resolutions of approximately 20 ps and approximately 10 $mu$m is also discussed. (auth